A plotbunny is the original idea that inspires someone to write a fic. Quite why they are called this is unknown.
Much badfic is caused by plotbunnies attacking at stupid times of the day or night; the story is then written and uploaded (for example, to the Pit of Voles) hurriedly, without a beta-read and often without even a second read-over by the author themselves. Any disgruntled reviewers wanting to know why the spelling is poor or the story just plain doesn't make sense are then directed to the disclaimer, where the author has announced that she wrote the fic in question at one in the morning, as if this is a) something to be proud of, and b) a reason to not tear her atrocious writing to shreds.
Plotbunnies are often found in humourfic either as cute, fluffy little rabbits (think Monty Python and the Holy Grail), or as terrifying man-sized creatures, akin to something from the film Donnie Darko. The former are often inspiration for cute fluff fics, the latter are the personification of badfic, and very dangerous. Plotbunnies do bite, and can be quite vicious.